That is non-convex. it would be non-convex (neither convex nor concave) even if X were real rather than complex. It would be non-convex, even if V were not raised to any power.
I don’t know how S is used in your model, so I can’t conclude that the model is non-convex. Perhaps there is a way of reformulating the code so as to never form S, but quite possibly, such a reformulation is not possible.
Your first task is proving the optimization problem is convex.